Your question:

Problem 4: (1 points) Decide whether a polynomial is irreducible x3+x2+x+1 (if coefficient operations are done mod 2). Hint: Brute force.

Assignment Help Answers with Step-by-Step Explanation:

b) x + 1

For (a), x is not a factor of x^3 + x^2 + x + 1.

c) x^2 + 1x + 0 = x^2 + x

d) x^2 + 1x + 1 = x^2 + x + 1

Since we've checked all possible linear and quadratic factors, and none of them are factors of x^3 + x^2 + x + 1, the polynomial x^3 + x^2 + x + 1 is irreducible over the field with coefficients done modulo 2.